Relatively Compact Sets of Heisenberg Manifolds

TL;DR

This paper establishes a precise criterion for when a set of left invariant metrics on a compact Heisenberg manifold is relatively compact within its moduli space, aiding in understanding the geometric structure of these manifolds.

Contribution

It provides a necessary and sufficient condition characterizing relative compactness of metric sets on compact Heisenberg manifolds in the moduli space.

Findings

Characterization of relative compactness in the moduli space

Necessary and sufficient condition for metric sets

Enhanced understanding of geometric structures on Heisenberg manifolds

Abstract

We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.